(19) Determine whether the following functions are injective, surjective, both, or neither. (a) f: RR defined by f(x) = eª. (b) g: Q→ R defined by g(x) = x³. (c) h: (0, ∞) → (0, 1] defined by h(x) = z²+1 (d) k: [0, ∞) → [7, ∞) defined by k(x) = x² + n.

Q: (5) Consider the several variable function f(x, y, z) = xe²y + yeš + ze¬². Give a general formula…

A: The given function,   fx,y,z=xe2y+ye3z+ze-x

Q: 3. Determine if the following functions are one-one. Explain why. •f: R R f(x) = (x - 2)² ● f:R R…

A: one- one function :Let f be a function which is one one if        x1≠x2   ⇒  f(x1) ≠ fx2 for every…

Q: Given f (x) = x² + 3, x > 0, find f and state any restrictions on the domain of f- (x). ON f-1(2) =…

A:

Q: Determine the domain for each of the following functions and sketch the domain. (a) f(x, y) = VT –…

A: The domain of a function is the set of all possible inputs for the function. We need to calculate…

Q: The set of all points where the function f(x) = x |x| is differentiable is (A) (-∞, ∞) (B) (-∞, 0) U…

A:

Q: Let f: 2,1 + R (the set of all real numbers) be a positive, non-constant and differentiable function…

A: Given:                          f:12,1→R It is a differentiable function such that…

Q: Make a sketch of the function f (t) defined by 0 5, 1, -1, f(1) = e(s-1), and express f in terms of…

A:

Q: (A) Suppose that f(x) is a real analytic function such that: Given this information find the best…

A:

Q: а. f (x) 3D x(4 — х)8 b. y = x² – ? 2 С. у %3D In (x + 1) — tan-1

A: Critical number

Q: [59] Evaluate F.dr where F(x.y)3y'i+(x-4)j and C is the portion of y=(x-1) from .x-0 to r-3.

A: Please see the explanation below

Q: eriodic function f (t) is defined by 2t, f (t) = [0, taro

A: we have to find the graph

Q: 1. Consider the periodic function f(x) that is defined over the interval (-x, 1) as f(-n < x < x) =…

A:

Q: Ax) %3D х* — Лх2 - 12x where A> = > — Лх? — ЛЕx where ^> v that fis one-to-one on S = [- rmine f(S).…

A: Given, fx=x3-λx2-λ2x,  λ&gt;0

Q: Determine which of the following functions are one-to-one. OA. f: R² R2 defined by f(x, y)= (x + y,…

A: Note - According to answering guidelines I will solve the first three parts. Pls post the other…

Q: Q.2: Find the interval in which the function is (a). Increasing, (b). Decreasing, (c). Concave Up,…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: 8. (p.241, #4) The function f: R → (0, 0) defined by f (x) = e**+1 is bijective. Find its inverse.

A: Replace f(x) with y.

Q: 5. (a) Let f: R R be defined by f(x) = x², let g: RR be defined by g(x) = sin x, and let h: R→ R be…

A: Step 15(a) The given functions are:f:R→R:f(x)=x2g:R→R:g(x)=sinxh:R→R:h(x)=3x​To find (h⋅(g⋅f))(x)…

Q: d. For each of the following, state whether the functions f: R → R, x → f(x) are injective,…

A: Given functions: fx=3x+2 fx=3x3-7x+3 fx=x6 fx=sinx fx=0.01x fx=4 We have to check whether the…

Q: 6. Define f(x) = x³ – Ax2 – 12x where A> 0 is a constant. (a) Show that f is one-to-one on S =…

A:

Q: 11. (a) Define f: RR by f(x) = x² - 4 for all x € R. Explain why the inverse of the function f is…

A: Step 1: Step 2:

Q: A nonnegative function f has domain (0, ∞). At each point P(x, y) on the graph of f, the tangent…

A: Given problem:- A nonnegative function f has domain (0, ∞). At each point P(x, y) on the graph of f,…

Q: 1. ƒ : (-∞, −16] → R, ƒ (x) R₁f(x) = ²+1 2. ƒ : (-∞, 0] → R, ƒ (x) = 3. ƒ: (-∞,0) → R, ƒ (x) = 1/x³…

A: Given :- Functions  To find :- For each of the following functions, state whether they are…

Q: The function f1 is defined by: f1(x) = 4Cos(x/2) , x E [0;4[ The function f2 is defined by: f2(x) =…

A:

Q: (x +1)4 – y² Let f(x, y) = { (x + 1)4 + y? - if (x, y) # (–1,0) -1 if (x, y) = (-1,0) a. Show that f…

A:

Q: • If f(x)= |sgn(x – 1)| then, 1. D; = R R; = {1,0, –1} 2. D; = [1,0) R; = {1,0} 3. D; = R R; = {1,0}…

A: We find domain and range of given functions